Answer :
Final answer:
The magnitude of the force that the shopper exerts 414 N.The work done on the cart by friction can be calculated using the formula: Work = force * displacement * cos(theta). The work done on the cart by the gravitational force is given by the formula: Work = m * g * h. The force the shopper exerts can be calculated using the formula: force = Work / (displacement * cos(theta)).
Explanation:
(a) To determine the work done on the cart by friction, we need to know the formula for work. Work is defined as the dot product of force and displacement. In this case, the frictional force is opposing the motion of the cart, so the work done on the cart by friction is negative. The formula for work is:
- Work = force * displacement * cos(theta)
Where:
force = magnitude of the force = 38.8 N,
displacement = distance traveled = 25.6 m,
theta = angle between force and displacement = 180° - 28.6° = 151.4°.
Plugging in the values, we can calculate the work done on the cart by friction:
- Work = 38.8 N * 25.6 m * cos(151.4°)
(b) The work done on the cart by the gravitational force is given by the formula:
- Work = m * g * h
Where:
- m = mass of the cart = 14.0 kg,
- g = acceleration due to gravity = 9.8 m/s^2,
- h = height of the cart = 0 (since it is on a flat horizontal surface).
Plugging in the values, we can calculate the work done on the cart by the gravitational force:
Work = 14.0 kg * 9.8 m/s^2 * 0
(c) The work done on the cart by the shopper can be calculated as the sum of the work done by friction and the work done by the gravitational force. Since these two forces are acting in opposite directions, the work done by the shopper will be the difference between the two:
- Work = Work(friction) - Work(gravity)
(d) To find the force the shopper exerts, we can use the formula for work:
Work = force * displacement * cos(theta)
We can rearrange this formula to solve for force:
force = Work / (displacement * cos(theta))
Plugging in the values, we can calculate the force the shopper exerts:
force = Work / (25.6 m * cos(28.6°))
(e) The total work done on the cart is the sum of the work done by friction and the work done by the gravitational force:
- Total Work = Work(friction) + Work(gravity)
- From calculating this we get,
The magnitude of the force that the shopper exerts 414 N.
